Annotated Bibliography of Resources for Educational Reform, Coherent Teaching Practice, and Improved Student Learning

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• Wheatley, G. H. (1993). The role of negotiation in mathematics learning. In K. Tobin (Ed.), The Practice of constructivism in science education (pp. 121-134). Washington: AAAS Press.

When instruction is informed by constructivism, negotiation plays a prominent role. This book chapter describes the negotiation between two ninth-grade boys who were in a mathematics program based on problem-centered learning. The goal of problem-centered learning is the construction of mathematics knowledge by students. The teacher selects tasks that have a high probability of being problematical for students, and the students work on the problems in small groups. The role of the teacher in this classroom is as a facilitator. Wheatley describes and analyzes an episode of negotiation between Brett and Sam as they worked on the solution of a problem. They held conflicting views about the solution and were attempting to come to a consensus. The negotiation process was complex because the two boys' intentions were different. Sam was generally ego-oriented, trying to "win" by following the rules without understanding. Brett, on the other hand, was task-oriented, trying to make sense of the problem. Wheatley asserts that teachers can increase the probability that meaningful learning will occur by creating classroom conditions where negotiation of mathematical meaning is the norm. In this case, a student like Sam could shift from his ego-orientation to a more productive stance.

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